Like any other writers, those who write for Star Trek try to make sure they get things right before the script goes to film. Of course, there are bound to be errors, but usually, fans can overlook them. They might point them out on Reddit, but, for the most part, we're okay with a bump in the road here and there...unless they really stand out because it's our field of expertise.
And that's exactly what happened during the fifth season of Star Trek: The Next Generation. After the season's sixteenth episode Ethics aired, a viewer wrote in with some corrections for Dr. Beverly Crusher [Gates McFadden], which were accurate and appreciated.
Andre Bormanis was the science consultant for the series and was trained in several sciences, but he understood they couldn't always get the tech stuff right. He told Deborah Fisher in the August/September 1997 edition of Star Trek Communicator, the Magazine for the Official Star Trek Fan Club that, after Ethics, they'd received a letter from a woman with a Ph.D. in pharmacology, correcting Dr. Crusher's orders and measurements when treating Worf [Michael Dorn] for his broken back.
Bormanis said "Dr. Crusher had ordered up 75 ccs of something that she pumped into Worf's carotid artery. This woman pointed out very astutely that 75 ccs is a lot of any fluid to pump into somebody's artery, even a Klingon. Plus medicine is measured in milligrams, and the hypospray Crusher was using could hold at the most 28 ccs of fluid." Bormanis appreciated the feedback, saying "that's the kind of good feedback I like because it helps to make the show better."
Star Trek isn't a medical show, but that one fan wanted to help make sure it was spot on with the medical facts as that was important to her. It would be no different than an engineer correcting Scotty's [James Doohan] calculations. But what's really great about this is that it shows Star Trek fans pay attention, and if we can, in some small way, make a show better, we make that effort. To this day, fans will still offer corrections or question the reasons behind an action one of the characters take. We're not being nitpicky; we just love the franchise that much and want it to be as right as possible.